In general in continuous casting for different types of steel and products of different dimensions or layouts, attention is directed to the growth of the solidifying strand shell only during the secondary cooling and to the position of the molten pool or sump tip in a deformation stretch. Thus it is known (EP 0 804 981 A) to squeeze the cast strand or billet in the deformation stretch so that the desired final thickness will result. For that purpose it is however only required to establish the position of the molten pool tip, based upon which the deformation force is applied horizontally along a wedge surface. Such a process is coarse and does not take into consideration the state of the lattice structure to be expected. The reasons lie in the disadvantageous heat distribution by disadvantageous cooling and a uniform strand bracing with nonuniform heat abstraction from the strand cross section. A matching of the secondary cooling to the strand support likewise is not to be found.